Towards the equivalence of Diffie-Hellman problem and discrete logarithm problem for important elliptic curves used in practice

Abstract

In this paper, we have improved the existing estimates of the minimum number of group operations required to solve Diffie-Hellman problem for important elliptic curves used in practice. This leads us towards the equivalence of Diffie-Hellman problem and the discrete logarithm problem for those important elliptic curves.